Using math to fight cancer

Engineers at the Georgia Institute of Technology are using integer
programming and computational optimization techniques in the fight against
prostate cancer. Mixed integer programming is a mathematical/optimization tool
in which problems are modeled into a mathematical formulation. The formulation
consists of variables that can be either continuous or integers.

Prostate brachytherapy requires implanting small radioactive
"seeds" in cancerous prostate. Planning treatment and deciding where seeds
should be placed is a manual and time-consuming procedure that takes hours of a
doctor's valuable time. But Eva Lee, an assistant professor of industrial and
systems engineering at the Georgia Institute of Technology and Emory
University's school of medicine, found a way to reduce the pre-planning to only
fifteen minutes.

Lee realized that the placement of the radioactive seeds is a
binary problem-a matter of deciding which of 300 possible locations is best for
seed implantation. Her use of mixed integer programming and optimization
techniques allows doctors to effectively manipulate the large number of
variables involved, such as shrinkage of the cancerous tumor over time and
distortion of the needles used for delivering the seeds.

"In the prostate cancer case, we formulate the treatment planning
into a mathematical model which includes all the clinical properties that we
would like to see in the plan,' says Lee. "We solve the model and the solution
tells us where to place the radioactive seeds inside the prostate."

Lee says her approach frees doctors from having to do the math
behind the seed placement. "All they have to do is tell the system what they
want in the plan," she says. She also indicates that the new approach should
help cut the recurrence rate for prostrate cancer and reduce toxicity in
adjacent healthy tissues.

The system is ready for commercialization, but has yet to receive
FDA approval. In addition to prostate cancer applications, the system may also
have applications for planning external beam radiation treatment for brain and
other types of cancer.

"Every sector in industry can benefit from the use of mixed
integer programming and optimization techniques," says Lee. Outside of medicine,
applications include in-vehicle routing and scheduling, and integrated circuit
design. For more information, contact Lee at eva.lee@isye.gatech.edu or call (404)
894-4962.

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